1. Technical Field
The present invention relates to a resonator element, and a resonator, an oscillator, an electronic device, and a moving object, each of which includes the resonator element.
2. Related Art
Hitherto, as a piezoelectric device represented by a piezoelectric resonator (an example of a resonator) or a piezoelectric oscillator (an example of an oscillator), a piezoelectric device is known which has a configuration in which, in a package having a tuning fork type piezoelectric resonator element (an example of a resonator element) fixed in a cantilever manner and accommodated therein, between two protrusions that are disposed in parallel at a predetermined interval and protrude inward, a folded remainder from a parent material, which protrudes from the center of an end portion of a base portion of the piezoelectric resonator element is accommodated (for example, refer to JP-A-2003-69368). The piezoelectric resonator element (hereinafter, referred to as a resonator element) used in the piezoelectric device has a configuration in which the folded remainder is provided in an engagement recessed portion which is provided at the end portion of the base portion and is engaged with the two protrusions in the package.
In recent years, to further reduce the size of the piezoelectric device, more reduction in the size of the resonator element is necessary. Regarding the resonator element, vibration leakage from the base portion due to the reduction in size is one of issues.
The vibration leakage will be described with reference to the drawings.
FIG. 15 is a schematic plan view illustrating the schematic configuration of the resonator element according to the related art. In addition, in the figure, the X-axis, the Y-axis, and the Z-axis are mutually perpendicular coordinate axes.
As illustrated in FIG. 15, the resonator element 91 according to the related art includes a base portion 92, and a pair of vibrating arms 93a and 93b that extend in parallel along the Y-axis direction from one end portion 92a of the base portion 92. An engagement recessed portion 94 that is recessed in the +(positive) Y direction is provided at the other end portion 92b on the opposite side to one end portion 92a of the base portion 92, and a folded remainder 95 from a parent material is provided to protrude from the center of the engagement recessed portion 94 in the − (negative) Y direction.
According to an analysis using a simulation by the inventors, in reaction to flexural vibration in which the resonator element 91 is displaced to be bent alternately in a direction indicated by the arrows A (a direction in which the pair of vibrating arms 93a and 93b are separated from each other) and in a direction indicated by the arrows B (a direction in which the pair of vibrating arms 93a and 93b approach each other) about the root portions of the pair of vibrating arms 93a and 93b as the fulcrums, forces in a direction indicated by the arrow C (the +Y direction) and in a direction indicated by the arrow D (the −Y direction) are alternately exerted on the base portion 92.
In detail, when the pair of vibrating arms 93a and 93b are bent in the direction indicated by the arrows A, a force F1 in a clockwise direction is exerted on the +X side from the center in the X-axis direction of the base portion 92 about the root portion of the vibrating arm 93a. 
On the other hand, a force F2 in a counterclockwise direction is exerted on the −X side from the center of the base portion 92 about the root portion of the vibrating arm 93b. 
Here, the components of the forces F1 and F2 in the X-axis direction cancel each other because the magnitudes of the forces are the same and the directions in which the forces are exerted are opposite to each other.
On the other hand, the components of the forces F1 and F2 in the Y-axis direction are added to each other and are exerted on the base portion 92 as a force in a direction indicated by the arrow C because the magnitudes of the forces are the same and the directions in which the forces are exerted are the same. Similarly, when the pair of vibrating arms 93a and 93b are bent in the direction indicated by the arrows B, a force F3 in the counterclockwise direction is exerted on the +X side from the center of the base portion 92 about the root portion of the vibrating arm 93a. 
On the other hand, a force F4 in the clockwise direction is exerted on the −X side from the center of the base portion 92 about the root portion of the vibrating arm 93b. 
Here, the components of the forces F3 and F4 in the X-axis direction cancel each other because the magnitudes of the forces are the same and the directions in which the forces are exerted are opposite to each other.
On the other hand, the components of the forces F3 and F4 in the Y-axis direction are added to each other and are exerted on the base portion 92 as a force in a direction indicated by the arrow D because the magnitudes of the forces are the same and the directions in which the forces are exerted are the same. In this case, since the engagement recessed portion 94 is provided in the base portion 92 of the resonator element 91, compared to a case where the engagement recessed portion 94 is not provided, the rigidity of the base portion 92 (particularly the rigidity of the center part) is reduced. Accordingly, the base portion 92 of the resonator element 91 cannot resist the forces in the direction indicated by the arrow C and the direction indicated by the arrow D and is displaced (vibrates) alternately in the direction indicated by the arrow C and in the direction indicated by the arrow D.
As a result, when the base portion 92 is fixed to a package (not illustrated) or the like, in the resonator element 91, a portion of vibrational energy generated by the flexural vibration of the pair of vibrating arms 93a and 93b leaks to the package or the like via a fixing member such as an adhesive that fixes the base portion 92 (vibration leakage).
As a measure to reduce the vibration leakage, for example, in a case where the engagement recessed portion 94 is removed so as to enhance the rigidity of the base portion 92, the folded remainder 95 directly protrudes from the other end portion 92b in the −Y direction.
As a result, in this measure, the size of the resonator element 91 in the Y-axis direction is increased, and thus there is a problem in that the measure goes against the reduction in the size.